Normal distribution worksheet with answers

Free printable Normal distribution worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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Name: ____________________ Date: ____________

1.Easy

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0582. Find z to two decimals.

A = 0.0582

z =

2.Easy

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction is above 50 points? Find P(X > x) as a decimal.

μ = 65σ = 10x = 50

P(X > x) =

3.Medium

X is normal with mean 60 s and standard deviation 5 s; Y is independent and normal with mean 45 s and standard deviation 4 s. Find the probability P that X + Y is more than 114.6 s. Round z to two decimals.

μ_X = 60, σ_X = 5μ_Y = 45, σ_Y = 4X + Y > 114.6 s

P =

4.Medium

The masses of boxes are independent and normal with mean 12 kg and standard deviation 0.8 kg. Find the probability P that the total mass of 16 of them exceeds 193.6 kg. Round z to two decimals.

μ = 12 kgσ = 0.8 kgn = 16> 193.6 kg

P =

5.Hard

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Find the value x below which 97.5% of them lie (the 97.5th percentile).

μ = 500σ = 40P = 97.5%

x = h

6.Hard

Runner A's lap time X and runner B's lap time Y are independent and normal: X has mean 52 s and standard deviation 4 s, Y has mean 48 s and standard deviation 3 s. Find the probability P that X is greater than Y. Round z to two decimals.

μ_X = 52 s, σ_X = 4 sμ_Y = 48 s, σ_Y = 3 s

P =

Answer key

1. z = −1.57
2. P(X > x) = 0.9332
3. P = 0.06681
4. P = 0.3085
5. x = 578.4 h
6. P = 0.7881

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